Graph Constructors#

Hiperwalk has specific commands (graph constructors) to generate instances of well-known specific graphs, such as Line, Cycle, and Grid. For a complete list of graph constructors, refer to List of Graph Constructors.

The key difference between creating an arbitrary graph and using a graph constructor is that for the former, you must explicitly provide the adjacency matrix. However, for the latter, the adjacency matrix is automatically generated based on specific graph parameters such as the number of vertices. Nevertheless, the order of neighbors is automatically embedded in the generated adjacency matrix.

For example, you can create a line with 10 vertices, a cycle with 10 vertices, and a grid of dimensions \(10 \times 10\) using valid commands, respectively.

>>> hpw.Line(10) 
<hiperwalk.graph.line.Line object at 0x7f0a6bb700d0>
>>> hpw.Cycle(10) 
<hiperwalk.graph.cycle.Cycle object at 0x7f0a6bbb32e0>
>>> hpw.Grid(10) 
<hiperwalk.graph.grid.Grid object at 0x7f0a6bbb2da0>

Naturally, you can create specific graphs using NetworkX and the hiperwalk.Graph class. Just be aware that the order of neighbors may vary, which may result in undesirable behavior, especially when dealing with coined quantum walks.

As an example, let’s consider a Line with 10 vertices. First, we create the line using the hiperwalk.Graph class.

>>> path = nx.path_graph(10)
>>> adj_matrix = nx.adjacency_matrix(path)
>>> arbitrary_line = hpw.Graph(adj_matrix)

Next, we create the line using the hiperwalk.Line graph constructor.

>>> graph_constructor_line = hpw.Line(10)

The order of neighbors os these two instances is different. For arbitrary_line, the neighbors are listed in ascending order, while for graph_constructor_line, the neighbors are listed in descending order (righmost neighbor followed by the leftmost neighbor).

>>> arbitrary_line.neighbors(1)
array([0, 2])
>>> graph_constructor_line.neighbors(1)
array([2, 0], dtype=int32)